LMFDB - Embedded newform 1078.2.e.m.177.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1078,2,Mod(67,1078)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1078, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1078.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1078 = 2 \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1078.e (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$8.60787333789$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 154)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			177.1
Root			$-0.707107 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	1078.177
Dual form			1078.2.e.m.67.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-1.20711 - 2.09077i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.292893 + 0.507306i) q^{5} +2.41421 q^{6} +1.00000 q^{8} +(-1.41421 + 2.44949i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-1.20711 - 2.09077i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.292893 + 0.507306i) q^{5} +2.41421 q^{6} +1.00000 q^{8} +(-1.41421 + 2.44949i) q^{9} +(-0.292893 - 0.507306i) q^{10} +(-0.500000 - 0.866025i) q^{11} +(-1.20711 + 2.09077i) q^{12} +3.82843 q^{13} +1.41421 q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.82843 + 3.16693i) q^{17} +(-1.41421 - 2.44949i) q^{18} +(-0.292893 + 0.507306i) q^{19} +0.585786 q^{20} +1.00000 q^{22} +(3.12132 - 5.40629i) q^{23} +(-1.20711 - 2.09077i) q^{24} +(2.32843 + 4.03295i) q^{25} +(-1.91421 + 3.31552i) q^{26} -0.414214 q^{27} +2.65685 q^{29} +(-0.707107 + 1.22474i) q^{30} +(-2.00000 - 3.46410i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-1.20711 + 2.09077i) q^{33} -3.65685 q^{34} +2.82843 q^{36} +(4.70711 - 8.15295i) q^{37} +(-0.292893 - 0.507306i) q^{38} +(-4.62132 - 8.00436i) q^{39} +(-0.292893 + 0.507306i) q^{40} +5.41421 q^{41} -5.65685 q^{43} +(-0.500000 + 0.866025i) q^{44} +(-0.828427 - 1.43488i) q^{45} +(3.12132 + 5.40629i) q^{46} +(-5.24264 + 9.08052i) q^{47} +2.41421 q^{48} -4.65685 q^{50} +(4.41421 - 7.64564i) q^{51} +(-1.91421 - 3.31552i) q^{52} +(-3.94975 - 6.84116i) q^{53} +(0.207107 - 0.358719i) q^{54} +0.585786 q^{55} +1.41421 q^{57} +(-1.32843 + 2.30090i) q^{58} +(-2.79289 - 4.83743i) q^{59} +(-0.707107 - 1.22474i) q^{60} +(5.91421 - 10.2437i) q^{61} +4.00000 q^{62} +1.00000 q^{64} +(-1.12132 + 1.94218i) q^{65} +(-1.20711 - 2.09077i) q^{66} +(-1.37868 - 2.38794i) q^{67} +(1.82843 - 3.16693i) q^{68} -15.0711 q^{69} -11.0711 q^{71} +(-1.41421 + 2.44949i) q^{72} +(-4.70711 - 8.15295i) q^{73} +(4.70711 + 8.15295i) q^{74} +(5.62132 - 9.73641i) q^{75} +0.585786 q^{76} +9.24264 q^{78} +(6.62132 - 11.4685i) q^{79} +(-0.292893 - 0.507306i) q^{80} +(4.74264 + 8.21449i) q^{81} +(-2.70711 + 4.68885i) q^{82} +12.1421 q^{83} -2.14214 q^{85} +(2.82843 - 4.89898i) q^{86} +(-3.20711 - 5.55487i) q^{87} +(-0.500000 - 0.866025i) q^{88} +(6.24264 - 10.8126i) q^{89} +1.65685 q^{90} -6.24264 q^{92} +(-4.82843 + 8.36308i) q^{93} +(-5.24264 - 9.08052i) q^{94} +(-0.171573 - 0.297173i) q^{95} +(-1.20711 + 2.09077i) q^{96} +3.82843 q^{97} +2.82843 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 2 q^{3} - 2 q^{4} - 4 q^{5} + 4 q^{6} + 4 q^{8}+O(q^{10}) $ 4 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 - 4 * q^5 + 4 * q^6 + 4 * q^8	$ 4 q - 2 q^{2} - 2 q^{3} - 2 q^{4} - 4 q^{5} + 4 q^{6} + 4 q^{8} - 4 q^{10} - 2 q^{11} - 2 q^{12} + 4 q^{13} - 2 q^{16} - 4 q^{17} - 4 q^{19} + 8 q^{20} + 4 q^{22} + 4 q^{23} - 2 q^{24} - 2 q^{25} - 2 q^{26} + 4 q^{27} - 12 q^{29} - 8 q^{31} - 2 q^{32} - 2 q^{33} + 8 q^{34} + 16 q^{37} - 4 q^{38} - 10 q^{39} - 4 q^{40} + 16 q^{41} - 2 q^{44} + 8 q^{45} + 4 q^{46} - 4 q^{47} + 4 q^{48} + 4 q^{50} + 12 q^{51} - 2 q^{52} + 4 q^{53} - 2 q^{54} + 8 q^{55} + 6 q^{58} - 14 q^{59} + 18 q^{61} + 16 q^{62} + 4 q^{64} + 4 q^{65} - 2 q^{66} - 14 q^{67} - 4 q^{68} - 32 q^{69} - 16 q^{71} - 16 q^{73} + 16 q^{74} + 14 q^{75} + 8 q^{76} + 20 q^{78} + 18 q^{79} - 4 q^{80} + 2 q^{81} - 8 q^{82} - 8 q^{83} + 48 q^{85} - 10 q^{87} - 2 q^{88} + 8 q^{89} - 16 q^{90} - 8 q^{92} - 8 q^{93} - 4 q^{94} - 12 q^{95} - 2 q^{96} + 4 q^{97}+O(q^{100}) $ 4 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 - 4 * q^5 + 4 * q^6 + 4 * q^8 - 4 * q^10 - 2 * q^11 - 2 * q^12 + 4 * q^13 - 2 * q^16 - 4 * q^17 - 4 * q^19 + 8 * q^20 + 4 * q^22 + 4 * q^23 - 2 * q^24 - 2 * q^25 - 2 * q^26 + 4 * q^27 - 12 * q^29 - 8 * q^31 - 2 * q^32 - 2 * q^33 + 8 * q^34 + 16 * q^37 - 4 * q^38 - 10 * q^39 - 4 * q^40 + 16 * q^41 - 2 * q^44 + 8 * q^45 + 4 * q^46 - 4 * q^47 + 4 * q^48 + 4 * q^50 + 12 * q^51 - 2 * q^52 + 4 * q^53 - 2 * q^54 + 8 * q^55 + 6 * q^58 - 14 * q^59 + 18 * q^61 + 16 * q^62 + 4 * q^64 + 4 * q^65 - 2 * q^66 - 14 * q^67 - 4 * q^68 - 32 * q^69 - 16 * q^71 - 16 * q^73 + 16 * q^74 + 14 * q^75 + 8 * q^76 + 20 * q^78 + 18 * q^79 - 4 * q^80 + 2 * q^81 - 8 * q^82 - 8 * q^83 + 48 * q^85 - 10 * q^87 - 2 * q^88 + 8 * q^89 - 16 * q^90 - 8 * q^92 - 8 * q^93 - 4 * q^94 - 12 * q^95 - 2 * q^96 + 4 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1078\mathbb{Z}\right)^\times$.

$n$	$199$	$981$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	−1.20711	−	2.09077i	−0.696923	−	1.20711i	−0.969528	−	0.244981i	$-0.921218\pi$
$3$	−1.20711	−	2.09077i	−0.696923	−	1.20711i	0.272605	−	0.962126i	$-0.412115\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−0.292893	+	0.507306i	−0.130986	+	0.226874i	−0.924057	−	0.382255i	$-0.875148\pi$
$5$	−0.292893	+	0.507306i	−0.130986	+	0.226874i	0.793071	+	0.609129i	$0.208481\pi$
$6$	2.41421			0.985599
$7$		0			0
$7$		0			0
$8$	1.00000			0.353553
$9$	−1.41421	+	2.44949i	−0.471405	+	0.816497i
$10$	−0.292893	−	0.507306i	−0.0926210	−	0.160424i
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$12$	−1.20711	+	2.09077i	−0.348462	+	0.603553i
$13$	3.82843			1.06181			0.530907	−	0.847430i	$-0.321851\pi$
$13$	3.82843			1.06181			0.530907	+	0.847430i	$0.321851\pi$
$14$		0			0
$15$	1.41421			0.365148
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.82843	+	3.16693i	0.443459	+	0.768093i	0.997943	−	0.0641009i	$-0.0204179\pi$
$17$	1.82843	+	3.16693i	0.443459	+	0.768093i	−0.554485	+	0.832194i	$0.687085\pi$
$18$	−1.41421	−	2.44949i	−0.333333	−	0.577350i
$19$	−0.292893	+	0.507306i	−0.0671943	+	0.116384i	−0.897665	−	0.440678i	$-0.854738\pi$
$19$	−0.292893	+	0.507306i	−0.0671943	+	0.116384i	0.830471	+	0.557062i	$0.188071\pi$
$20$	0.585786			0.130986
$21$		0			0
$22$	1.00000			0.213201
$23$	3.12132	−	5.40629i	0.650840	−	1.12729i	−0.332079	−	0.943252i	$-0.607750\pi$
$23$	3.12132	−	5.40629i	0.650840	−	1.12729i	0.982919	−	0.184037i	$-0.0589166\pi$
$24$	−1.20711	−	2.09077i	−0.246400	−	0.426777i
$25$	2.32843	+	4.03295i	0.465685	+	0.806591i
$26$	−1.91421	+	3.31552i	−0.375408	+	0.650226i
$27$	−0.414214			−0.0797154
$28$		0			0
$29$	2.65685			0.493365			0.246683	−	0.969096i	$-0.420659\pi$
$29$	2.65685			0.493365			0.246683	+	0.969096i	$0.420659\pi$
$30$	−0.707107	+	1.22474i	−0.129099	+	0.223607i
$31$	−2.00000	−	3.46410i	−0.359211	−	0.622171i	0.628619	−	0.777714i	$-0.283621\pi$
$31$	−2.00000	−	3.46410i	−0.359211	−	0.622171i	−0.987829	+	0.155543i	$0.950287\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−1.20711	+	2.09077i	−0.210130	+	0.363956i
$34$	−3.65685			−0.627145
$35$		0			0
$36$	2.82843			0.471405
$37$	4.70711	−	8.15295i	0.773844	−	1.34034i	−0.161599	−	0.986857i	$-0.551665\pi$
$37$	4.70711	−	8.15295i	0.773844	−	1.34034i	0.935442	−	0.353480i	$-0.115002\pi$
$38$	−0.292893	−	0.507306i	−0.0475136	−	0.0822959i
$39$	−4.62132	−	8.00436i	−0.740003	−	1.28172i
$40$	−0.292893	+	0.507306i	−0.0463105	+	0.0802121i
$41$	5.41421			0.845558			0.422779	−	0.906233i	$-0.361055\pi$
$41$	5.41421			0.845558			0.422779	+	0.906233i	$0.361055\pi$
$42$		0			0
$43$	−5.65685			−0.862662			−0.431331	−	0.902194i	$-0.641956\pi$
$43$	−5.65685			−0.862662			−0.431331	+	0.902194i	$0.641956\pi$
$44$	−0.500000	+	0.866025i	−0.0753778	+	0.130558i
$45$	−0.828427	−	1.43488i	−0.123495	−	0.213899i
$46$	3.12132	+	5.40629i	0.460214	+	0.797113i
$47$	−5.24264	+	9.08052i	−0.764718	+	1.32453i	0.175678	+	0.984448i	$0.443788\pi$
$47$	−5.24264	+	9.08052i	−0.764718	+	1.32453i	−0.940396	+	0.340082i	$0.889545\pi$
$48$	2.41421			0.348462
$49$		0			0
$50$	−4.65685			−0.658579
$51$	4.41421	−	7.64564i	0.618114	−	1.07060i
$52$	−1.91421	−	3.31552i	−0.265454	−	0.459779i
$53$	−3.94975	−	6.84116i	−0.542540	−	0.939706i	−0.998757	−	0.0498379i	$-0.984130\pi$
$53$	−3.94975	−	6.84116i	−0.542540	−	0.939706i	0.456218	−	0.889868i	$-0.349204\pi$
$54$	0.207107	−	0.358719i	0.0281837	−	0.0488155i
$55$	0.585786			0.0789874
$56$		0			0
$57$	1.41421			0.187317
$58$	−1.32843	+	2.30090i	−0.174431	+	0.302123i
$59$	−2.79289	−	4.83743i	−0.363604	−	0.629780i	0.624947	−	0.780667i	$-0.285120\pi$
$59$	−2.79289	−	4.83743i	−0.363604	−	0.629780i	−0.988551	+	0.150887i	$0.951787\pi$
$60$	−0.707107	−	1.22474i	−0.0912871	−	0.158114i
$61$	5.91421	−	10.2437i	0.757237	−	1.31157i	−0.187017	−	0.982357i	$-0.559882\pi$
$61$	5.91421	−	10.2437i	0.757237	−	1.31157i	0.944254	−	0.329217i	$-0.106785\pi$
$62$	4.00000			0.508001
$63$		0			0
$64$	1.00000			0.125000
$65$	−1.12132	+	1.94218i	−0.139083	+	0.240898i
$66$	−1.20711	−	2.09077i	−0.148585	−	0.257356i
$67$	−1.37868	−	2.38794i	−0.168433	−	0.291734i	0.769436	−	0.638723i	$-0.220537\pi$
$67$	−1.37868	−	2.38794i	−0.168433	−	0.291734i	−0.937869	+	0.346990i	$0.887204\pi$
$68$	1.82843	−	3.16693i	0.221729	−	0.384047i
$69$	−15.0711			−1.81434
$70$		0			0
$71$	−11.0711			−1.31389			−0.656947	−	0.753937i	$-0.728152\pi$
$71$	−11.0711			−1.31389			−0.656947	+	0.753937i	$0.728152\pi$
$72$	−1.41421	+	2.44949i	−0.166667	+	0.288675i
$73$	−4.70711	−	8.15295i	−0.550925	−	0.954230i	−0.998208	−	0.0598379i	$-0.980942\pi$
$73$	−4.70711	−	8.15295i	−0.550925	−	0.954230i	0.447283	−	0.894393i	$-0.352392\pi$
$74$	4.70711	+	8.15295i	0.547190	+	0.947761i
$75$	5.62132	−	9.73641i	0.649094	−	1.12426i
$76$	0.585786			0.0671943
$77$		0			0
$78$	9.24264			1.04652
$79$	6.62132	−	11.4685i	0.744957	−	1.29030i	−0.205258	−	0.978708i	$-0.565803\pi$
$79$	6.62132	−	11.4685i	0.744957	−	1.29030i	0.950215	−	0.311595i	$-0.100863\pi$
$80$	−0.292893	−	0.507306i	−0.0327465	−	0.0567185i
$81$	4.74264	+	8.21449i	0.526960	+	0.912722i
$82$	−2.70711	+	4.68885i	−0.298950	+	0.517796i
$83$	12.1421			1.33277			0.666386	−	0.745607i	$-0.267840\pi$
$83$	12.1421			1.33277			0.666386	+	0.745607i	$0.267840\pi$
$84$		0			0
$85$	−2.14214			−0.232347
$86$	2.82843	−	4.89898i	0.304997	−	0.528271i
$87$	−3.20711	−	5.55487i	−0.343838	−	0.595545i
$88$	−0.500000	−	0.866025i	−0.0533002	−	0.0923186i
$89$	6.24264	−	10.8126i	0.661719	−	1.14613i	−0.318445	−	0.947941i	$-0.603161\pi$
$89$	6.24264	−	10.8126i	0.661719	−	1.14613i	0.980164	−	0.198189i	$-0.0635060\pi$
$90$	1.65685			0.174648
$91$		0			0
$92$	−6.24264			−0.650840
$93$	−4.82843	+	8.36308i	−0.500685	+	0.867211i
$94$	−5.24264	−	9.08052i	−0.540737	−	0.936584i
$95$	−0.171573	−	0.297173i	−0.0176030	−	0.0304893i
$96$	−1.20711	+	2.09077i	−0.123200	+	0.213388i
$97$	3.82843			0.388718			0.194359	−	0.980930i	$-0.437737\pi$
$97$	3.82843			0.388718			0.194359	+	0.980930i	$0.437737\pi$
$98$		0			0
$99$	2.82843			0.284268
$100$	2.32843	−	4.03295i	0.232843	−	0.403295i
$101$	3.08579	+	5.34474i	0.307047	+	0.531821i	0.977715	−	0.209936i	$-0.0673257\pi$
$101$	3.08579	+	5.34474i	0.307047	+	0.531821i	−0.670668	+	0.741758i	$0.733992\pi$
$102$	4.41421	+	7.64564i	0.437072	+	0.757031i
$103$	6.70711	−	11.6170i	0.660871	−	1.14466i	−0.319516	−	0.947581i	$-0.603520\pi$
$103$	6.70711	−	11.6170i	0.660871	−	1.14466i	0.980387	−	0.197081i	$-0.0631462\pi$
$104$	3.82843			0.375408
$105$		0			0
$106$	7.89949			0.767267
$107$	1.53553	−	2.65962i	0.148446	−	0.257115i	−0.782207	−	0.623018i	$-0.785906\pi$
$107$	1.53553	−	2.65962i	0.148446	−	0.257115i	0.930653	+	0.365903i	$0.119240\pi$
$108$	0.207107	+	0.358719i	0.0199289	+	0.0345178i
$109$	−8.24264	−	14.2767i	−0.789502	−	1.36746i	−0.926272	−	0.376854i	$-0.877006\pi$
$109$	−8.24264	−	14.2767i	−0.789502	−	1.36746i	0.136771	−	0.990603i	$-0.456328\pi$
$110$	−0.292893	+	0.507306i	−0.0279263	+	0.0483697i
$111$	−22.7279			−2.15724
$112$		0			0
$113$	−8.17157			−0.768717			−0.384358	−	0.923184i	$-0.625577\pi$
$113$	−8.17157			−0.768717			−0.384358	+	0.923184i	$0.625577\pi$
$114$	−0.707107	+	1.22474i	−0.0662266	+	0.114708i
$115$	1.82843	+	3.16693i	0.170502	+	0.295318i
$116$	−1.32843	−	2.30090i	−0.123341	−	0.213634i
$117$	−5.41421	+	9.37769i	−0.500544	+	0.866968i
$118$	5.58579			0.514213
$119$		0			0
$120$	1.41421			0.129099
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$	5.91421	+	10.2437i	0.535448	+	0.927423i
$123$	−6.53553	−	11.3199i	−0.589289	−	1.02068i
$124$	−2.00000	+	3.46410i	−0.179605	+	0.311086i
$125$	−5.65685			−0.505964
$126$		0			0
$127$	15.7279			1.39563			0.697814	−	0.716279i	$-0.254156\pi$
$127$	15.7279			1.39563			0.697814	+	0.716279i	$0.254156\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	6.82843	+	11.8272i	0.601209	+	1.04133i
$130$	−1.12132	−	1.94218i	−0.0983463	−	0.170341i
$131$	−0.292893	+	0.507306i	−0.0255902	+	0.0443235i	−0.878537	−	0.477674i	$-0.841480\pi$
$131$	−0.292893	+	0.507306i	−0.0255902	+	0.0443235i	0.852947	+	0.521998i	$0.174813\pi$
$132$	2.41421			0.210130
$133$		0			0
$134$	2.75736			0.238200
$135$	0.121320	−	0.210133i	0.0104416	−	0.0180854i
$136$	1.82843	+	3.16693i	0.156786	+	0.271562i
$137$	8.32843	+	14.4253i	0.711546	+	1.23243i	0.964277	+	0.264897i	$0.0853378\pi$
$137$	8.32843	+	14.4253i	0.711546	+	1.23243i	−0.252731	+	0.967537i	$0.581329\pi$
$138$	7.53553	−	13.0519i	0.641467	−	1.11105i
$139$		0			0			−	1.00000i	$-0.5\pi$
$139$		0			0				1.00000i	$0.5\pi$
$140$		0			0
$141$	25.3137			2.13180
$142$	5.53553	−	9.58783i	0.464532	−	0.804592i
$143$	−1.91421	−	3.31552i	−0.160075	−	0.277257i
$144$	−1.41421	−	2.44949i	−0.117851	−	0.204124i
$145$	−0.778175	+	1.34784i	−0.0646239	+	0.111932i
$146$	9.41421			0.779126
$147$		0			0
$148$	−9.41421			−0.773844
$149$	−8.82843	+	15.2913i	−0.723253	+	1.25271i	0.236436	+	0.971647i	$0.424021\pi$
$149$	−8.82843	+	15.2913i	−0.723253	+	1.25271i	−0.959689	+	0.281064i	$0.909313\pi$
$150$	5.62132	+	9.73641i	0.458979	+	0.794975i
$151$	7.86396	+	13.6208i	0.639960	+	1.10844i	0.985441	+	0.170018i	$0.0543825\pi$
$151$	7.86396	+	13.6208i	0.639960	+	1.10844i	−0.345481	+	0.938426i	$0.612284\pi$
$152$	−0.292893	+	0.507306i	−0.0237568	+	0.0411479i
$153$	−10.3431			−0.836194
$154$		0			0
$155$	2.34315			0.188206
$156$	−4.62132	+	8.00436i	−0.370002	+	0.640862i
$157$	8.82843	+	15.2913i	0.704585	+	1.22038i	0.966841	+	0.255379i	$0.0822002\pi$
$157$	8.82843	+	15.2913i	0.704585	+	1.22038i	−0.262256	+	0.964998i	$0.584466\pi$
$158$	6.62132	+	11.4685i	0.526764	+	0.912382i
$159$	−9.53553	+	16.5160i	−0.756217	+	1.30981i
$160$	0.585786			0.0463105
$161$		0			0
$162$	−9.48528			−0.745234
$163$	−4.86396	+	8.42463i	−0.380975	+	0.659868i	−0.991202	−	0.132359i	$-0.957745\pi$
$163$	−4.86396	+	8.42463i	−0.380975	+	0.659868i	0.610227	+	0.792227i	$0.291078\pi$
$164$	−2.70711	−	4.68885i	−0.211390	−	0.366137i
$165$	−0.707107	−	1.22474i	−0.0550482	−	0.0953463i
$166$	−6.07107	+	10.5154i	−0.471206	+	0.816153i
$167$	−13.7279			−1.06230			−0.531149	−	0.847278i	$-0.678240\pi$
$167$	−13.7279			−1.06230			−0.531149	+	0.847278i	$0.678240\pi$
$168$		0			0
$169$	1.65685			0.127450
$170$	1.07107	−	1.85514i	0.0821472	−	0.142283i
$171$	−0.828427	−	1.43488i	−0.0633514	−	0.109728i
$172$	2.82843	+	4.89898i	0.215666	+	0.373544i
$173$	−4.91421	+	8.51167i	−0.373621	+	0.647130i	−0.990120	−	0.140226i	$-0.955217\pi$
$173$	−4.91421	+	8.51167i	−0.373621	+	0.647130i	0.616499	+	0.787356i	$0.288551\pi$
$174$	6.41421			0.486260
$175$		0			0
$176$	1.00000			0.0753778
$177$	−6.74264	+	11.6786i	−0.506808	+	0.877817i
$178$	6.24264	+	10.8126i	0.467906	+	0.810436i
$179$	−0.449747	−	0.778985i	−0.0336157	−	0.0582241i	0.848728	−	0.528829i	$-0.177369\pi$
$179$	−0.449747	−	0.778985i	−0.0336157	−	0.0582241i	−0.882344	+	0.470605i	$0.844036\pi$
$180$	−0.828427	+	1.43488i	−0.0617473	+	0.106949i
$181$	7.65685			0.569129			0.284565	−	0.958657i	$-0.408151\pi$
$181$	7.65685			0.569129			0.284565	+	0.958657i	$0.408151\pi$
$182$		0			0
$183$	−28.5563			−2.11095
$184$	3.12132	−	5.40629i	0.230107	−	0.398557i
$185$	2.75736	+	4.77589i	0.202725	+	0.351130i
$186$	−4.82843	−	8.36308i	−0.354037	−	0.613211i
$187$	1.82843	−	3.16693i	0.133708	−	0.231589i
$188$	10.4853			0.764718
$189$		0			0
$190$	0.343146			0.0248944
$191$	3.58579	−	6.21076i	0.259458	−	0.449395i	−0.706639	−	0.707575i	$-0.749789\pi$
$191$	3.58579	−	6.21076i	0.259458	−	0.449395i	0.966097	+	0.258180i	$0.0831226\pi$
$192$	−1.20711	−	2.09077i	−0.0871154	−	0.150888i
$193$	−10.9497	−	18.9655i	−0.788180	−	1.36517i	−0.927081	−	0.374862i	$-0.877690\pi$
$193$	−10.9497	−	18.9655i	−0.788180	−	1.36517i	0.138901	−	0.990306i	$-0.455643\pi$
$194$	−1.91421	+	3.31552i	−0.137433	+	0.238040i
$195$	5.41421			0.387720
$196$		0			0
$197$	−0.514719			−0.0366722			−0.0183361	−	0.999832i	$-0.505837\pi$
$197$	−0.514719			−0.0366722			−0.0183361	+	0.999832i	$0.505837\pi$
$198$	−1.41421	+	2.44949i	−0.100504	+	0.174078i
$199$	0.0502525	+	0.0870399i	0.00356231	+	0.00617010i	0.867801	−	0.496912i	$-0.165533\pi$
$199$	0.0502525	+	0.0870399i	0.00356231	+	0.00617010i	−0.864239	+	0.503082i	$0.832199\pi$
$200$	2.32843	+	4.03295i	0.164645	+	0.285173i
$201$	−3.32843	+	5.76500i	−0.234769	+	0.406632i
$202$	−6.17157			−0.434230
$203$		0			0
$204$	−8.82843			−0.618114
$205$	−1.58579	+	2.74666i	−0.110756	+	0.191835i
$206$	6.70711	+	11.6170i	0.467306	+	0.809398i
$207$	8.82843	+	15.2913i	0.613618	+	1.06282i
$208$	−1.91421	+	3.31552i	−0.132727	+	0.229890i
$209$	0.585786			0.0405197
$210$		0			0
$211$	7.41421			0.510416			0.255208	−	0.966886i	$-0.417856\pi$
$211$	7.41421			0.510416			0.255208	+	0.966886i	$0.417856\pi$
$212$	−3.94975	+	6.84116i	−0.271270	+	0.469853i
$213$	13.3640	+	23.1471i	0.915684	+	1.58601i
$214$	1.53553	+	2.65962i	0.104967	+	0.181808i
$215$	1.65685	−	2.86976i	0.112997	−	0.195716i
$216$	−0.414214			−0.0281837
$217$		0			0
$218$	16.4853			1.11652
$219$	−11.3640	+	19.6830i	−0.767905	+	1.33005i
$220$	−0.292893	−	0.507306i	−0.0197469	−	0.0342026i
$221$	7.00000	+	12.1244i	0.470871	+	0.815572i
$222$	11.3640	−	19.6830i	0.762699	−	1.32103i
$223$	−8.58579			−0.574947			−0.287473	−	0.957789i	$-0.592815\pi$
$223$	−8.58579			−0.574947			−0.287473	+	0.957789i	$0.592815\pi$
$224$		0			0
$225$	−13.1716			−0.878105
$226$	4.08579	−	7.07679i	0.271782	−	0.470741i
$227$	−14.4142	−	24.9662i	−0.956705	−	1.65706i	−0.730417	−	0.683001i	$-0.760674\pi$
$227$	−14.4142	−	24.9662i	−0.956705	−	1.65706i	−0.226288	−	0.974061i	$-0.572659\pi$
$228$	−0.707107	−	1.22474i	−0.0468293	−	0.0811107i
$229$	11.6569	−	20.1903i	0.770307	−	1.33421i	−0.167088	−	0.985942i	$-0.553436\pi$
$229$	11.6569	−	20.1903i	0.770307	−	1.33421i	0.937395	−	0.348268i	$-0.113230\pi$
$230$	−3.65685			−0.241126
$231$		0			0
$232$	2.65685			0.174431
$233$	−0.707107	+	1.22474i	−0.0463241	+	0.0802357i	−0.888258	−	0.459345i	$-0.848084\pi$
$233$	−0.707107	+	1.22474i	−0.0463241	+	0.0802357i	0.841934	+	0.539581i	$0.181417\pi$
$234$	−5.41421	−	9.37769i	−0.353938	−	0.613039i
$235$	−3.07107	−	5.31925i	−0.200334	−	0.346989i
$236$	−2.79289	+	4.83743i	−0.181802	+	0.314890i
$237$	−31.9706			−2.07671
$238$		0			0
$239$	20.2132			1.30748			0.653742	−	0.756718i	$-0.273198\pi$
$239$	20.2132			1.30748			0.653742	+	0.756718i	$0.273198\pi$
$240$	−0.707107	+	1.22474i	−0.0456435	+	0.0790569i
$241$	6.12132	+	10.6024i	0.394309	+	0.682963i	0.993013	−	0.118007i	$-0.0376507\pi$
$241$	6.12132	+	10.6024i	0.394309	+	0.682963i	−0.598704	+	0.800971i	$0.704317\pi$
$242$	−0.500000	−	0.866025i	−0.0321412	−	0.0556702i
$243$	10.8284	−	18.7554i	0.694644	−	1.20316i
$244$	−11.8284			−0.757237
$245$		0			0
$246$	13.0711			0.833381
$247$	−1.12132	+	1.94218i	−0.0713479	+	0.123578i
$248$	−2.00000	−	3.46410i	−0.127000	−	0.219971i
$249$	−14.6569	−	25.3864i	−0.928840	−	1.60880i
$250$	2.82843	−	4.89898i	0.178885	−	0.309839i
$251$	26.1421			1.65008			0.825038	−	0.565077i	$-0.191153\pi$
$251$	26.1421			1.65008			0.825038	+	0.565077i	$0.191153\pi$
$252$		0			0
$253$	−6.24264			−0.392471
$254$	−7.86396	+	13.6208i	−0.493429	+	0.854644i
$255$	2.58579	+	4.47871i	0.161928	+	0.280468i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−12.5711	+	21.7737i	−0.784162	+	1.35821i	0.145337	+	0.989382i	$0.453573\pi$
$257$	−12.5711	+	21.7737i	−0.784162	+	1.35821i	−0.929499	+	0.368826i	$0.879760\pi$
$258$	−13.6569			−0.850239
$259$		0			0
$260$	2.24264			0.139083
$261$	−3.75736	+	6.50794i	−0.232575	+	0.402831i
$262$	−0.292893	−	0.507306i	−0.0180950	−	0.0313415i
$263$	8.52082	+	14.7585i	0.525416	+	0.910047i	0.999562	+	0.0296008i	$0.00942362\pi$
$263$	8.52082	+	14.7585i	0.525416	+	0.910047i	−0.474146	+	0.880446i	$0.657243\pi$
$264$	−1.20711	+	2.09077i	−0.0742923	+	0.128678i
$265$	4.62742			0.284260
$266$		0			0
$267$	−30.1421			−1.84467
$268$	−1.37868	+	2.38794i	−0.0842163	+	0.145867i
$269$	1.17157	+	2.02922i	0.0714321	+	0.123724i	0.899529	−	0.436861i	$-0.143910\pi$
$269$	1.17157	+	2.02922i	0.0714321	+	0.123724i	−0.828097	+	0.560585i	$0.810576\pi$
$270$	0.121320	+	0.210133i	0.00738332	+	0.0127883i
$271$	2.27817	−	3.94591i	0.138389	−	0.239697i	−0.788498	−	0.615038i	$-0.789141\pi$
$271$	2.27817	−	3.94591i	0.138389	−	0.239697i	0.926887	+	0.375340i	$0.122474\pi$
$272$	−3.65685			−0.221729
$273$		0			0
$274$	−16.6569			−1.00628
$275$	2.32843	−	4.03295i	0.140409	−	0.243196i
$276$	7.53553	+	13.0519i	0.453586	+	0.785634i
$277$	−0.914214	−	1.58346i	−0.0549298	−	0.0951412i	0.837253	−	0.546816i	$-0.184160\pi$
$277$	−0.914214	−	1.58346i	−0.0549298	−	0.0951412i	−0.892183	+	0.451675i	$0.850827\pi$
$278$		0			0
$279$	11.3137			0.677334
$280$		0			0
$281$	8.72792			0.520664			0.260332	−	0.965519i	$-0.416168\pi$
$281$	8.72792			0.520664			0.260332	+	0.965519i	$0.416168\pi$
$282$	−12.6569	+	21.9223i	−0.753705	+	1.30545i
$283$	−11.7071	−	20.2773i	−0.695915	−	1.20536i	−0.969871	−	0.243618i	$-0.921666\pi$
$283$	−11.7071	−	20.2773i	−0.695915	−	1.20536i	0.273956	−	0.961742i	$-0.411668\pi$
$284$	5.53553	+	9.58783i	0.328474	+	0.568933i
$285$	−0.414214	+	0.717439i	−0.0245359	+	0.0424974i
$286$	3.82843			0.226380
$287$		0			0
$288$	2.82843			0.166667
$289$	1.81371	−	3.14144i	0.106689	−	0.184790i
$290$	−0.778175	−	1.34784i	−0.0456960	−	0.0791478i
$291$	−4.62132	−	8.00436i	−0.270907	−	0.469224i
$292$	−4.70711	+	8.15295i	−0.275463	+	0.477115i
$293$	10.8284			0.632603			0.316302	−	0.948659i	$-0.397559\pi$
$293$	10.8284			0.632603			0.316302	+	0.948659i	$0.397559\pi$
$294$		0			0
$295$	3.27208			0.190508
$296$	4.70711	−	8.15295i	0.273595	−	0.473880i
$297$	0.207107	+	0.358719i	0.0120176	+	0.0208150i
$298$	−8.82843	−	15.2913i	−0.511417	−	0.885800i
$299$	11.9497	−	20.6976i	0.691072	−	1.19697i
$300$	−11.2426			−0.649094
$301$		0			0
$302$	−15.7279			−0.905040
$303$	7.44975	−	12.9033i	0.427977	−	0.741278i
$304$	−0.292893	−	0.507306i	−0.0167986	−	0.0290960i
$305$	3.46447	+	6.00063i	0.198375	+	0.343595i
$306$	5.17157	−	8.95743i	0.295639	−	0.512062i
$307$	−9.89949			−0.564994			−0.282497	−	0.959268i	$-0.591163\pi$
$307$	−9.89949			−0.564994			−0.282497	+	0.959268i	$0.591163\pi$
$308$		0			0
$309$	−32.3848			−1.84231
$310$	−1.17157	+	2.02922i	−0.0665409	+	0.115252i
$311$	8.36396	+	14.4868i	0.474277	+	0.821471i	0.999566	−	0.0294522i	$-0.00937629\pi$
$311$	8.36396	+	14.4868i	0.474277	+	0.821471i	−0.525289	+	0.850924i	$0.676043\pi$
$312$	−4.62132	−	8.00436i	−0.261631	−	0.453158i
$313$	−10.3284	+	17.8894i	−0.583797	+	1.01117i	0.411227	+	0.911533i	$0.365100\pi$
$313$	−10.3284	+	17.8894i	−0.583797	+	1.01117i	−0.995024	+	0.0996335i	$0.968233\pi$
$314$	−17.6569			−0.996434
$315$		0			0
$316$	−13.2426			−0.744957
$317$	−4.34315	+	7.52255i	−0.243935	+	0.422508i	−0.961832	−	0.273642i	$-0.911772\pi$
$317$	−4.34315	+	7.52255i	−0.243935	+	0.422508i	0.717896	+	0.696150i	$0.245105\pi$
$318$	−9.53553	−	16.5160i	−0.534726	−	0.926173i
$319$	−1.32843	−	2.30090i	−0.0743776	−	0.128826i
$320$	−0.292893	+	0.507306i	−0.0163732	+	0.0283593i
$321$	−7.41421			−0.413821
$322$		0			0
$323$	−2.14214			−0.119192
$324$	4.74264	−	8.21449i	0.263480	−	0.456361i
$325$	8.91421	+	15.4399i	0.494472	+	0.856450i
$326$	−4.86396	−	8.42463i	−0.269390	−	0.466597i
$327$	−19.8995	+	34.4669i	−1.10044	+	1.90603i
$328$	5.41421			0.298950
$329$		0			0
$330$	1.41421			0.0778499
$331$	12.0355	−	20.8462i	0.661533	−	1.14581i	−0.318680	−	0.947862i	$-0.603240\pi$
$331$	12.0355	−	20.8462i	0.661533	−	1.14581i	0.980213	−	0.197946i	$-0.0634271\pi$
$332$	−6.07107	−	10.5154i	−0.333193	−	0.577107i
$333$	13.3137	+	23.0600i	0.729587	+	1.26368i
$334$	6.86396	−	11.8887i	0.375579	−	0.650522i
$335$	1.61522			0.0882491
$336$		0			0
$337$	−28.2426			−1.53847			−0.769237	−	0.638963i	$-0.779364\pi$
$337$	−28.2426			−1.53847			−0.769237	+	0.638963i	$0.779364\pi$
$338$	−0.828427	+	1.43488i	−0.0450605	+	0.0780471i
$339$	9.86396	+	17.0849i	0.535737	+	0.927923i
$340$	1.07107	+	1.85514i	0.0580868	+	0.100609i
$341$	−2.00000	+	3.46410i	−0.108306	+	0.187592i
$342$	1.65685			0.0895924
$343$		0			0
$344$	−5.65685			−0.304997
$345$	4.41421	−	7.64564i	0.237653	−	0.411628i
$346$	−4.91421	−	8.51167i	−0.264190	−	0.457590i
$347$	−8.70711	−	15.0812i	−0.467422	−	0.809599i	0.531885	−	0.846816i	$-0.321484\pi$
$347$	−8.70711	−	15.0812i	−0.467422	−	0.809599i	−0.999307	+	0.0372179i	$0.988150\pi$
$348$	−3.20711	+	5.55487i	−0.171919	+	0.297772i
$349$		0			0			−	1.00000i	$-0.5\pi$
$349$		0			0				1.00000i	$0.5\pi$
$350$		0			0
$351$	−1.58579			−0.0846430
$352$	−0.500000	+	0.866025i	−0.0266501	+	0.0461593i
$353$	−1.34315	−	2.32640i	−0.0714884	−	0.123822i	0.828065	−	0.560632i	$-0.189442\pi$
$353$	−1.34315	−	2.32640i	−0.0714884	−	0.123822i	−0.899554	+	0.436810i	$0.856108\pi$
$354$	−6.74264	−	11.6786i	−0.358367	−	0.620710i
$355$	3.24264	−	5.61642i	0.172101	−	0.298089i
$356$	−12.4853			−0.661719
$357$		0			0
$358$	0.899495			0.0475398
$359$	−9.62132	+	16.6646i	−0.507794	+	0.879525i	0.492165	+	0.870502i	$0.336206\pi$
$359$	−9.62132	+	16.6646i	−0.507794	+	0.879525i	−0.999959	+	0.00902308i	$0.997128\pi$
$360$	−0.828427	−	1.43488i	−0.0436619	−	0.0756247i
$361$	9.32843	+	16.1573i	0.490970	+	0.850385i
$362$	−3.82843	+	6.63103i	−0.201218	+	0.348519i
$363$	2.41421			0.126713
$364$		0			0
$365$	5.51472			0.288654
$366$	14.2782	−	24.7305i	0.746332	−	1.29269i
$367$	−5.36396	−	9.29065i	−0.279996	−	0.484968i	0.691387	−	0.722485i	$-0.257000\pi$
$367$	−5.36396	−	9.29065i	−0.279996	−	0.484968i	−0.971384	+	0.237516i	$0.923667\pi$
$368$	3.12132	+	5.40629i	0.162710	+	0.281822i
$369$	−7.65685	+	13.2621i	−0.398600	+	0.690395i
$370$	−5.51472			−0.286697
$371$		0			0
$372$	9.65685			0.500685
$373$	9.98528	−	17.2950i	0.517018	−	0.895502i	−0.482786	−	0.875738i	$-0.660375\pi$
$373$	9.98528	−	17.2950i	0.517018	−	0.895502i	0.999805	−	0.0197638i	$-0.00629142\pi$
$374$	1.82843	+	3.16693i	0.0945457	+	0.163758i
$375$	6.82843	+	11.8272i	0.352618	+	0.610753i
$376$	−5.24264	+	9.08052i	−0.270369	+	0.468292i
$377$	10.1716			0.523863
$378$		0			0
$379$	27.8701			1.43159			0.715794	−	0.698311i	$-0.246065\pi$
$379$	27.8701			1.43159			0.715794	+	0.698311i	$0.246065\pi$
$380$	−0.171573	+	0.297173i	−0.00880150	+	0.0152447i
$381$	−18.9853	−	32.8835i	−0.972645	−	1.68467i
$382$	3.58579	+	6.21076i	0.183465	+	0.317770i
$383$	−3.19239	+	5.52938i	−0.163123	+	0.282538i	−0.935987	−	0.352034i	$-0.885490\pi$
$383$	−3.19239	+	5.52938i	−0.163123	+	0.282538i	0.772864	+	0.634572i	$0.218824\pi$
$384$	2.41421			0.123200
$385$		0			0
$386$	21.8995			1.11465
$387$	8.00000	−	13.8564i	0.406663	−	0.704361i
$388$	−1.91421	−	3.31552i	−0.0971795	−	0.168320i
$389$	11.3640	+	19.6830i	0.576176	+	0.997966i	0.995913	+	0.0903199i	$0.0287889\pi$
$389$	11.3640	+	19.6830i	0.576176	+	0.997966i	−0.419737	+	0.907646i	$0.637878\pi$
$390$	−2.70711	+	4.68885i	−0.137080	+	0.237429i
$391$	22.8284			1.15448
$392$		0			0
$393$	1.41421			0.0713376
$394$	0.257359	−	0.445759i	0.0129656	−	0.0224570i
$395$	3.87868	+	6.71807i	0.195158	+	0.338023i
$396$	−1.41421	−	2.44949i	−0.0710669	−	0.123091i
$397$	11.0000	−	19.0526i	0.552074	−	0.956221i	−0.446051	−	0.895008i	$-0.647170\pi$
$397$	11.0000	−	19.0526i	0.552074	−	0.956221i	0.998125	−	0.0612128i	$-0.0194968\pi$
$398$	−0.100505			−0.00503786
$399$		0			0
$400$	−4.65685			−0.232843
$401$	−9.15685	+	15.8601i	−0.457271	+	0.792017i	−0.998816	−	0.0486549i	$-0.984507\pi$
$401$	−9.15685	+	15.8601i	−0.457271	+	0.792017i	0.541544	+	0.840672i	$0.317840\pi$
$402$	−3.32843	−	5.76500i	−0.166007	−	0.287532i
$403$	−7.65685	−	13.2621i	−0.381415	−	0.660630i
$404$	3.08579	−	5.34474i	0.153524	−	0.265911i
$405$	−5.55635			−0.276097
$406$		0			0
$407$	−9.41421			−0.466645
$408$	4.41421	−	7.64564i	0.218536	−	0.378516i
$409$	1.36396	+	2.36245i	0.0674435	+	0.116816i	0.897775	−	0.440454i	$-0.145182\pi$
$409$	1.36396	+	2.36245i	0.0674435	+	0.116816i	−0.830332	+	0.557269i	$0.811849\pi$
$410$	−1.58579	−	2.74666i	−0.0783164	−	0.135648i
$411$	20.1066	−	34.8257i	0.991786	−	1.71782i
$412$	−13.4142			−0.660871
$413$		0			0
$414$	−17.6569			−0.867787
$415$	−3.55635	+	6.15978i	−0.174574	+	0.302372i
$416$	−1.91421	−	3.31552i	−0.0938520	−	0.162557i
$417$		0			0
$418$	−0.292893	+	0.507306i	−0.0143259	+	0.0248131i
$419$	26.1421			1.27713			0.638563	−	0.769569i	$-0.279529\pi$
$419$	26.1421			1.27713			0.638563	+	0.769569i	$0.279529\pi$
$420$		0			0
$421$	0.686292			0.0334478			0.0167239	−	0.999860i	$-0.494676\pi$
$421$	0.686292			0.0334478			0.0167239	+	0.999860i	$0.494676\pi$
$422$	−3.70711	+	6.42090i	−0.180459	+	0.312564i
$423$	−14.8284	−	25.6836i	−0.720983	−	1.24878i
$424$	−3.94975	−	6.84116i	−0.191817	−	0.332236i
$425$	−8.51472	+	14.7479i	−0.413025	+	0.715379i
$426$	−26.7279			−1.29497
$427$		0			0
$428$	−3.07107			−0.148446
$429$	−4.62132	+	8.00436i	−0.223119	+	0.386454i
$430$	1.65685	+	2.86976i	0.0799006	+	0.138392i
$431$	8.79289	+	15.2297i	0.423539	+	0.733591i	0.996283	−	0.0861437i	$-0.0274544\pi$
$431$	8.79289	+	15.2297i	0.423539	+	0.733591i	−0.572744	+	0.819734i	$0.694121\pi$
$432$	0.207107	−	0.358719i	0.00996443	−	0.0172589i
$433$	−26.1421			−1.25631			−0.628155	−	0.778088i	$-0.716190\pi$
$433$	−26.1421			−1.25631			−0.628155	+	0.778088i	$0.716190\pi$
$434$		0			0
$435$	3.75736			0.180152
$436$	−8.24264	+	14.2767i	−0.394751	+	0.683729i
$437$	1.82843	+	3.16693i	0.0874655	+	0.151495i
$438$	−11.3640	−	19.6830i	−0.542991	−	0.940488i
$439$	−13.6924	+	23.7159i	−0.653502	+	1.13190i	0.328765	+	0.944412i	$0.393368\pi$
$439$	−13.6924	+	23.7159i	−0.653502	+	1.13190i	−0.982267	+	0.187487i	$0.939966\pi$
$440$	0.585786			0.0279263
$441$		0			0
$442$	−14.0000			−0.665912
$443$	−6.31371	+	10.9357i	−0.299973	+	0.519569i	−0.976130	−	0.217189i	$-0.930311\pi$
$443$	−6.31371	+	10.9357i	−0.299973	+	0.519569i	0.676156	+	0.736758i	$0.263644\pi$
$444$	11.3640	+	19.6830i	0.539310	+	0.934112i
$445$	3.65685	+	6.33386i	0.173352	+	0.300254i
$446$	4.29289	−	7.43551i	0.203274	−	0.352082i
$447$	42.6274			2.01621
$448$		0			0
$449$	22.3431			1.05444			0.527219	−	0.849729i	$-0.323235\pi$
$449$	22.3431			1.05444			0.527219	+	0.849729i	$0.323235\pi$
$450$	6.58579	−	11.4069i	0.310457	−	0.537727i
$451$	−2.70711	−	4.68885i	−0.127473	−	0.220789i
$452$	4.08579	+	7.07679i	0.192179	+	0.332864i
$453$	18.9853	−	32.8835i	0.892006	−	1.54500i
$454$	28.8284			1.35299
$455$		0			0
$456$	1.41421			0.0662266
$457$	5.82843	−	10.0951i	0.272642	−	0.472230i	−0.696895	−	0.717173i	$-0.745436\pi$
$457$	5.82843	−	10.0951i	0.272642	−	0.472230i	0.969538	+	0.244943i	$0.0787691\pi$
$458$	11.6569	+	20.1903i	0.544689	+	0.943429i
$459$	−0.757359	−	1.31178i	−0.0353505	−	0.0612289i
$460$	1.82843	−	3.16693i	0.0852509	−	0.147659i
$461$	8.31371			0.387208			0.193604	−	0.981080i	$-0.437982\pi$
$461$	8.31371			0.387208			0.193604	+	0.981080i	$0.437982\pi$
$462$		0			0
$463$	12.8284			0.596188			0.298094	−	0.954537i	$-0.403649\pi$
$463$	12.8284			0.596188			0.298094	+	0.954537i	$0.403649\pi$
$464$	−1.32843	+	2.30090i	−0.0616707	+	0.106817i
$465$	−2.82843	−	4.89898i	−0.131165	−	0.227185i
$466$	−0.707107	−	1.22474i	−0.0327561	−	0.0567352i
$467$	−17.0000	+	29.4449i	−0.786666	+	1.36255i	0.141332	+	0.989962i	$0.454861\pi$
$467$	−17.0000	+	29.4449i	−0.786666	+	1.36255i	−0.927999	+	0.372584i	$0.878472\pi$
$468$	10.8284			0.500544
$469$		0			0
$470$	6.14214			0.283316
$471$	21.3137	−	36.9164i	0.982084	−	1.70102i
$472$	−2.79289	−	4.83743i	−0.128553	−	0.222661i
$473$	2.82843	+	4.89898i	0.130051	+	0.225255i
$474$	15.9853	−	27.6873i	0.734228	−	1.27172i
$475$	−2.72792			−0.125166
$476$		0			0
$477$	22.3431			1.02302
$478$	−10.1066	+	17.5051i	−0.462265	+	0.800667i
$479$	−5.96447	−	10.3308i	−0.272523	−	0.472024i	0.696984	−	0.717087i	$-0.254525\pi$
$479$	−5.96447	−	10.3308i	−0.272523	−	0.472024i	−0.969507	+	0.245062i	$0.921192\pi$
$480$	−0.707107	−	1.22474i	−0.0322749	−	0.0559017i
$481$	18.0208	−	31.2130i	0.821678	−	1.42319i
$482$	−12.2426			−0.557637
$483$		0			0
$484$	1.00000			0.0454545
$485$	−1.12132	+	1.94218i	−0.0509165	+	0.0881900i
$486$	10.8284	+	18.7554i	0.491187	+	0.850762i
$487$	4.82843	+	8.36308i	0.218797	+	0.378967i	0.954440	−	0.298402i	$-0.0964534\pi$
$487$	4.82843	+	8.36308i	0.218797	+	0.378967i	−0.735644	+	0.677369i	$0.763120\pi$
$488$	5.91421	−	10.2437i	0.267724	−	0.463711i
$489$	23.4853			1.06204
$490$		0			0
$491$	19.1716			0.865201			0.432600	−	0.901586i	$-0.357596\pi$
$491$	19.1716			0.865201			0.432600	+	0.901586i	$0.357596\pi$
$492$	−6.53553	+	11.3199i	−0.294645	+	0.510339i
$493$	4.85786	+	8.41407i	0.218787	+	0.378951i
$494$	−1.12132	−	1.94218i	−0.0504506	−	0.0873830i
$495$	−0.828427	+	1.43488i	−0.0372350	+	0.0644930i
$496$	4.00000			0.179605
$497$		0			0
$498$	29.3137			1.31358
$499$	−11.0711	+	19.1757i	−0.495609	+	0.858420i	−0.999987	−	0.00506282i	$-0.998388\pi$
$499$	−11.0711	+	19.1757i	−0.495609	+	0.858420i	0.504378	+	0.863483i	$0.331722\pi$
$500$	2.82843	+	4.89898i	0.126491	+	0.219089i
$501$	16.5711	+	28.7019i	0.740341	+	1.28231i
$502$	−13.0711	+	22.6398i	−0.583390	+	1.01046i
$503$	−4.21320			−0.187857			−0.0939287	−	0.995579i	$-0.529943\pi$
$503$	−4.21320			−0.187857			−0.0939287	+	0.995579i	$0.529943\pi$
$504$		0			0
$505$	−3.61522			−0.160875
$506$	3.12132	−	5.40629i	0.138760	−	0.240339i
$507$	−2.00000	−	3.46410i	−0.0888231	−	0.153846i
$508$	−7.86396	−	13.6208i	−0.348907	−	0.604324i
$509$	4.65685	−	8.06591i	0.206411	−	0.357515i	−0.744170	−	0.667990i	$-0.767155\pi$
$509$	4.65685	−	8.06591i	0.206411	−	0.357515i	0.950582	+	0.310475i	$0.100488\pi$
$510$	−5.17157			−0.229001
$511$		0			0
$512$	1.00000			0.0441942
$513$	0.121320	−	0.210133i	0.00535642	−	0.00927760i
$514$	−12.5711	−	21.7737i	−0.554486	−	0.960398i
$515$	3.92893	+	6.80511i	0.173129	+	0.299869i
$516$	6.82843	−	11.8272i	0.300605	−	0.520663i
$517$	10.4853			0.461142
$518$		0			0
$519$	23.7279			1.04154
$520$	−1.12132	+	1.94218i	−0.0491731	+	0.0851704i
$521$	−14.1421	−	24.4949i	−0.619578	−	1.07314i	−0.989563	−	0.144103i	$-0.953970\pi$
$521$	−14.1421	−	24.4949i	−0.619578	−	1.07314i	0.369984	−	0.929038i	$-0.379363\pi$
$522$	−3.75736	−	6.50794i	−0.164455	−	0.284845i
$523$	−6.36396	+	11.0227i	−0.278277	+	0.481989i	−0.970957	−	0.239256i	$-0.923097\pi$
$523$	−6.36396	+	11.0227i	−0.278277	+	0.481989i	0.692680	+	0.721245i	$0.256430\pi$
$524$	0.585786			0.0255902
$525$		0			0
$526$	−17.0416			−0.743050
$527$	7.31371	−	12.6677i	0.318590	−	0.551814i
$528$	−1.20711	−	2.09077i	−0.0525326	−	0.0909891i
$529$	−7.98528	−	13.8309i	−0.347186	−	0.601344i
$530$	−2.31371	+	4.00746i	−0.100501	+	0.174073i
$531$	15.7990			0.685618
$532$		0			0
$533$	20.7279			0.897826
$534$	15.0711	−	26.1039i	0.652189	−	1.12962i
$535$	0.899495	+	1.55797i	0.0388886	+	0.0673570i
$536$	−1.37868	−	2.38794i	−0.0595499	−	0.103143i
$537$	−1.08579	+	1.88064i	−0.0468551	+	0.0811555i
$538$	−2.34315			−0.101020
$539$		0			0
$540$	−0.242641			−0.0104416
$541$	6.42893	−	11.1352i	0.276401	−	0.478741i	−0.694086	−	0.719892i	$-0.744191\pi$
$541$	6.42893	−	11.1352i	0.276401	−	0.478741i	0.970488	+	0.241151i	$0.0775248\pi$
$542$	2.27817	+	3.94591i	0.0978560	+	0.169492i
$543$	−9.24264	−	16.0087i	−0.396640	−	0.687000i
$544$	1.82843	−	3.16693i	0.0783932	−	0.135781i
$545$	9.65685			0.413654
$546$		0			0
$547$	34.8701			1.49094			0.745468	−	0.666541i	$-0.232226\pi$
$547$	34.8701			1.49094			0.745468	+	0.666541i	$0.232226\pi$
$548$	8.32843	−	14.4253i	0.355773	−	0.616217i
$549$	16.7279	+	28.9736i	0.713930	+	1.23656i
$550$	2.32843	+	4.03295i	0.0992845	+	0.171966i
$551$	−0.778175	+	1.34784i	−0.0331514	+	0.0574198i
$552$	−15.0711			−0.641467
$553$		0			0
$554$	1.82843			0.0776824
$555$	6.65685	−	11.5300i	0.282568	−	0.489422i
$556$		0			0
$557$	−3.75736	−	6.50794i	−0.159204	−	0.275750i	0.775378	−	0.631498i	$-0.217560\pi$
$557$	−3.75736	−	6.50794i	−0.159204	−	0.275750i	−0.934582	+	0.355748i	$0.884226\pi$
$558$	−5.65685	+	9.79796i	−0.239474	+	0.414781i
$559$	−21.6569			−0.915987
$560$		0			0
$561$	−8.82843			−0.372736
$562$	−4.36396	+	7.55860i	−0.184083	+	0.318840i
$563$	4.53553	+	7.85578i	0.191150	+	0.331081i	0.945632	−	0.325240i	$-0.105445\pi$
$563$	4.53553	+	7.85578i	0.191150	+	0.331081i	−0.754482	+	0.656321i	$0.772112\pi$
$564$	−12.6569	−	21.9223i	−0.532950	−	0.923096i
$565$	2.39340	−	4.14549i	0.100691	−	0.174402i
$566$	23.4142			0.984173
$567$		0			0
$568$	−11.0711			−0.464532
$569$	2.00000	−	3.46410i	0.0838444	−	0.145223i	−0.821054	−	0.570851i	$-0.806613\pi$
$569$	2.00000	−	3.46410i	0.0838444	−	0.145223i	0.904898	+	0.425628i	$0.139947\pi$
$570$	−0.414214	−	0.717439i	−0.0173495	−	0.0300502i
$571$	−13.1924	−	22.8499i	−0.552084	−	0.956238i	−0.998124	−	0.0612248i	$-0.980499\pi$
$571$	−13.1924	−	22.8499i	−0.552084	−	0.956238i	0.446040	−	0.895013i	$-0.352834\pi$
$572$	−1.91421	+	3.31552i	−0.0800373	+	0.138629i
$573$	−17.3137			−0.723291
$574$		0			0
$575$	29.0711			1.21235
$576$	−1.41421	+	2.44949i	−0.0589256	+	0.102062i
$577$	−4.84315	−	8.38857i	−0.201623	−	0.349221i	0.747429	−	0.664342i	$-0.231288\pi$
$577$	−4.84315	−	8.38857i	−0.201623	−	0.349221i	−0.949051	+	0.315121i	$0.897955\pi$
$578$	1.81371	+	3.14144i	0.0754403	+	0.130666i
$579$	−26.4350	+	45.7868i	−1.09860	+	1.90284i
$580$	1.55635			0.0646239
$581$		0			0
$582$	9.24264			0.383120
$583$	−3.94975	+	6.84116i	−0.163582	+	0.283332i
$584$	−4.70711	−	8.15295i	−0.194781	−	0.337371i
$585$	−3.17157	−	5.49333i	−0.131128	−	0.227121i
$586$	−5.41421	+	9.37769i	−0.223659	+	0.387389i
$587$	25.1005			1.03601			0.518004	−	0.855378i	$-0.326675\pi$
$587$	25.1005			1.03601			0.518004	+	0.855378i	$0.326675\pi$
$588$		0			0
$589$	2.34315			0.0965476
$590$	−1.63604	+	2.83370i	−0.0673547	+	0.116662i
$591$	0.621320	+	1.07616i	0.0255577	+	0.0442672i
$592$	4.70711	+	8.15295i	0.193461	+	0.335084i
$593$	11.8492	−	20.5235i	0.486590	−	0.842799i	−0.513291	−	0.858215i	$-0.671574\pi$
$593$	11.8492	−	20.5235i	0.486590	−	0.842799i	0.999881	+	0.0154159i	$0.00490721\pi$
$594$	−0.414214			−0.0169954
$595$		0			0
$596$	17.6569			0.723253
$597$	0.121320	−	0.210133i	0.00496531	−	0.00860017i
$598$	11.9497	+	20.6976i	0.488662	+	0.846387i
$599$	−21.3137	−	36.9164i	−0.870855	−	1.50836i	−0.861114	−	0.508412i	$-0.830233\pi$
$599$	−21.3137	−	36.9164i	−0.870855	−	1.50836i	−0.00974040	−	0.999953i	$-0.503101\pi$
$600$	5.62132	−	9.73641i	0.229489	−	0.397487i
$601$	−31.9411			−1.30291			−0.651453	−	0.758689i	$-0.725840\pi$
$601$	−31.9411			−1.30291			−0.651453	+	0.758689i	$0.725840\pi$
$602$		0			0
$603$	7.79899			0.317599
$604$	7.86396	−	13.6208i	0.319980	−	0.554222i
$605$	−0.292893	−	0.507306i	−0.0119078	−	0.0206249i
$606$	7.44975	+	12.9033i	0.302625	+	0.524162i
$607$	−21.4853	+	37.2136i	−0.872061	+	1.51045i	−0.0121994	+	0.999926i	$0.503883\pi$
$607$	−21.4853	+	37.2136i	−0.872061	+	1.51045i	−0.859861	+	0.510528i	$0.829450\pi$
$608$	0.585786			0.0237568
$609$		0			0
$610$	−6.92893			−0.280544
$611$	−20.0711	+	34.7641i	−0.811988	+	1.40641i
$612$	5.17157	+	8.95743i	0.209048	+	0.362083i
$613$	−14.3137	−	24.7921i	−0.578125	−	1.00134i	−0.995694	−	0.0926971i	$-0.970451\pi$
$613$	−14.3137	−	24.7921i	−0.578125	−	1.00134i	0.417569	−	0.908645i	$-0.362882\pi$
$614$	4.94975	−	8.57321i	0.199756	−	0.345987i
$615$	7.65685			0.308754
$616$		0			0
$617$	−41.9706			−1.68967			−0.844836	−	0.535026i	$-0.820302\pi$
$617$	−41.9706			−1.68967			−0.844836	+	0.535026i	$0.820302\pi$
$618$	16.1924	−	28.0460i	0.651353	−	1.12818i
$619$	−10.9706	−	19.0016i	−0.440944	−	0.763738i	0.556816	−	0.830636i	$-0.312023\pi$
$619$	−10.9706	−	19.0016i	−0.440944	−	0.763738i	−0.997760	+	0.0668984i	$0.978690\pi$
$620$	−1.17157	−	2.02922i	−0.0470515	−	0.0814956i
$621$	−1.29289	+	2.23936i	−0.0518820	+	0.0898623i
$622$	−16.7279			−0.670729
$623$		0			0
$624$	9.24264			0.370002
$625$	−9.98528	+	17.2950i	−0.399411	+	0.691801i
$626$	−10.3284	−	17.8894i	−0.412807	−	0.715003i
$627$	−0.707107	−	1.22474i	−0.0282391	−	0.0489116i
$628$	8.82843	−	15.2913i	0.352293	−	0.610189i
$629$	34.4264			1.37267
$630$		0			0
$631$	23.2721			0.926447			0.463223	−	0.886242i	$-0.346693\pi$
$631$	23.2721			0.926447			0.463223	+	0.886242i	$0.346693\pi$
$632$	6.62132	−	11.4685i	0.263382	−	0.456191i
$633$	−8.94975	−	15.5014i	−0.355721	−	0.616126i
$634$	−4.34315	−	7.52255i	−0.172488	−	0.298759i
$635$	−4.60660	+	7.97887i	−0.182807	+	0.316632i
$636$	19.0711			0.756217
$637$		0			0
$638$	2.65685			0.105186
$639$	15.6569	−	27.1185i	0.619376	−	1.07279i
$640$	−0.292893	−	0.507306i	−0.0115776	−	0.0200530i
$641$	−7.64214	−	13.2366i	−0.301846	−	0.522813i	0.674708	−	0.738085i	$-0.264270\pi$
$641$	−7.64214	−	13.2366i	−0.301846	−	0.522813i	−0.976554	+	0.215272i	$0.930936\pi$
$642$	3.70711	−	6.42090i	0.146308	−	0.253413i
$643$	−1.58579			−0.0625373			−0.0312687	−	0.999511i	$-0.509955\pi$
$643$	−1.58579			−0.0625373			−0.0312687	+	0.999511i	$0.509955\pi$
$644$		0			0
$645$	−8.00000			−0.315000
$646$	1.07107	−	1.85514i	0.0421406	−	0.0729897i
$647$	15.0919	+	26.1399i	0.593323	+	1.02767i	0.993781	+	0.111351i	$0.0355177\pi$
$647$	15.0919	+	26.1399i	0.593323	+	1.02767i	−0.400458	+	0.916315i	$0.631149\pi$
$648$	4.74264	+	8.21449i	0.186309	+	0.322696i
$649$	−2.79289	+	4.83743i	−0.109631	+	0.189886i
$650$	−17.8284			−0.699288
$651$		0			0
$652$	9.72792			0.380975
$653$	9.19239	−	15.9217i	0.359726	−	0.623064i	−0.628189	−	0.778061i	$-0.716204\pi$
$653$	9.19239	−	15.9217i	0.359726	−	0.623064i	0.987915	+	0.154997i	$0.0495369\pi$
$654$	−19.8995	−	34.4669i	−0.778132	−	1.34776i
$655$	−0.171573	−	0.297173i	−0.00670391	−	0.0116115i
$656$	−2.70711	+	4.68885i	−0.105695	+	0.183069i
$657$	26.6274			1.03883
$658$		0			0
$659$	−12.0000			−0.467454			−0.233727	−	0.972302i	$-0.575092\pi$
$659$	−12.0000			−0.467454			−0.233727	+	0.972302i	$0.575092\pi$
$660$	−0.707107	+	1.22474i	−0.0275241	+	0.0476731i
$661$	9.48528	+	16.4290i	0.368935	+	0.639014i	0.989399	−	0.145221i	$-0.0463893\pi$
$661$	9.48528	+	16.4290i	0.368935	+	0.639014i	−0.620465	+	0.784234i	$0.713056\pi$
$662$	12.0355	+	20.8462i	0.467774	+	0.810209i
$663$	16.8995	−	29.2708i	0.656322	−	1.13678i
$664$	12.1421			0.471206
$665$		0			0
$666$	−26.6274			−1.03179
$667$	8.29289	−	14.3637i	0.321102	−	0.556165i
$668$	6.86396	+	11.8887i	0.265575	+	0.459989i
$669$	10.3640	+	17.9509i	0.400694	+	0.694022i
$670$	−0.807612	+	1.39882i	−0.0312008	+	0.0540413i
$671$	−11.8284			−0.456631
$672$		0			0
$673$	5.55635			0.214182			0.107091	−	0.994249i	$-0.465846\pi$
$673$	5.55635			0.214182			0.107091	+	0.994249i	$0.465846\pi$
$674$	14.1213	−	24.4588i	0.543933	−	0.942119i
$675$	−0.964466	−	1.67050i	−0.0371223	−	0.0642977i
$676$	−0.828427	−	1.43488i	−0.0318626	−	0.0551876i
$677$	−17.6569	+	30.5826i	−0.678608	+	1.17538i	0.296792	+	0.954942i	$0.404083\pi$
$677$	−17.6569	+	30.5826i	−0.678608	+	1.17538i	−0.975400	+	0.220441i	$0.929250\pi$
$678$	−19.7279			−0.757646
$679$		0			0
$680$	−2.14214			−0.0821472
$681$	−34.7990	+	60.2736i	−1.33350	+	2.30969i
$682$	−2.00000	−	3.46410i	−0.0765840	−	0.132647i
$683$	−6.79289	−	11.7656i	−0.259923	−	0.450200i	0.706298	−	0.707914i	$-0.250364\pi$
$683$	−6.79289	−	11.7656i	−0.259923	−	0.450200i	−0.966221	+	0.257715i	$0.917030\pi$
$684$	−0.828427	+	1.43488i	−0.0316757	+	0.0548639i
$685$	−9.75736			−0.372810
$686$		0			0
$687$	−56.2843			−2.14738
$688$	2.82843	−	4.89898i	0.107833	−	0.186772i
$689$	−15.1213	−	26.1909i	−0.576076	−	0.997794i
$690$	4.41421	+	7.64564i	0.168046	+	0.291065i
$691$	14.0355	−	24.3103i	0.533937	−	0.924806i	−0.465277	−	0.885165i	$-0.654045\pi$
$691$	14.0355	−	24.3103i	0.533937	−	0.924806i	0.999214	−	0.0396407i	$-0.0126213\pi$
$692$	9.82843			0.373621
$693$		0			0
$694$	17.4142			0.661035
$695$		0			0
$696$	−3.20711	−	5.55487i	−0.121565	−	0.210557i
$697$	9.89949	+	17.1464i	0.374970	+	0.649467i
$698$		0			0
$699$	3.41421			0.129137
$700$		0			0
$701$	−26.1127			−0.986263			−0.493132	−	0.869955i	$-0.664148\pi$
$701$	−26.1127			−0.986263			−0.493132	+	0.869955i	$0.664148\pi$
$702$	0.792893	−	1.37333i	0.0299258	−	0.0518331i
$703$	2.75736	+	4.77589i	0.103996	+	0.180126i
$704$	−0.500000	−	0.866025i	−0.0188445	−	0.0326396i
$705$	−7.41421	+	12.8418i	−0.279235	+	0.483650i
$706$	2.68629			0.101100
$707$		0			0
$708$	13.4853			0.506808
$709$	6.02082	−	10.4284i	0.226116	−	0.391645i	−0.730537	−	0.682873i	$-0.760730\pi$
$709$	6.02082	−	10.4284i	0.226116	−	0.391645i	0.956654	+	0.291228i	$0.0940637\pi$
$710$	3.24264	+	5.61642i	0.121694	+	0.210780i
$711$	18.7279	+	32.4377i	0.702352	+	1.21651i
$712$	6.24264	−	10.8126i	0.233953	−	0.405218i
$713$	−24.9706			−0.935155
$714$		0			0
$715$	2.24264			0.0838700
$716$	−0.449747	+	0.778985i	−0.0168079	+	0.0291121i
$717$	−24.3995	−	42.2612i	−0.911216	−	1.57827i
$718$	−9.62132	−	16.6646i	−0.359064	−	0.621918i
$719$	−0.757359	+	1.31178i	−0.0282447	+	0.0489213i	−0.879802	−	0.475340i	$-0.842325\pi$
$719$	−0.757359	+	1.31178i	−0.0282447	+	0.0489213i	0.851558	+	0.524261i	$0.175658\pi$
$720$	1.65685			0.0617473
$721$		0			0
$722$	−18.6569			−0.694336
$723$	14.7782	−	25.5965i	0.549606	−	0.951946i
$724$	−3.82843	−	6.63103i	−0.142282	−	0.246440i
$725$	6.18629	+	10.7150i	0.229753	+	0.397944i
$726$	−1.20711	+	2.09077i	−0.0447999	+	0.0775958i
$727$	−36.4264			−1.35098			−0.675490	−	0.737369i	$-0.736068\pi$
$727$	−36.4264			−1.35098			−0.675490	+	0.737369i	$0.736068\pi$
$728$		0			0
$729$	−23.8284			−0.882534
$730$	−2.75736	+	4.77589i	−0.102054	+	0.176763i
$731$	−10.3431	−	17.9149i	−0.382555	−	0.662605i
$732$	14.2782	+	24.7305i	0.527737	+	0.914066i
$733$	−6.50000	+	11.2583i	−0.240083	+	0.415836i	−0.960738	−	0.277458i	$-0.910508\pi$
$733$	−6.50000	+	11.2583i	−0.240083	+	0.415836i	0.720655	+	0.693294i	$0.243841\pi$
$734$	10.7279			0.395975
$735$		0			0
$736$	−6.24264			−0.230107
$737$	−1.37868	+	2.38794i	−0.0507843	+	0.0879610i
$738$	−7.65685	−	13.2621i	−0.281853	−	0.488183i
$739$	26.2132	+	45.4026i	0.964268	+	1.67016i	0.711568	+	0.702617i	$0.247985\pi$
$739$	26.2132	+	45.4026i	0.964268	+	1.67016i	0.252700	+	0.967545i	$0.418681\pi$
$740$	2.75736	−	4.77589i	0.101363	−	0.175565i
$741$	5.41421			0.198896
$742$		0			0
$743$	−13.3137			−0.488433			−0.244216	−	0.969721i	$-0.578531\pi$
$743$	−13.3137			−0.488433			−0.244216	+	0.969721i	$0.578531\pi$
$744$	−4.82843	+	8.36308i	−0.177019	+	0.306605i
$745$	−5.17157	−	8.95743i	−0.189472	−	0.328175i
$746$	9.98528	+	17.2950i	0.365587	+	0.633215i
$747$	−17.1716	+	29.7420i	−0.628275	+	1.08820i
$748$	−3.65685			−0.133708
$749$		0			0
$750$	−13.6569			−0.498678
$751$	−22.8284	+	39.5400i	−0.833021	+	1.44283i	0.0626103	+	0.998038i	$0.480057\pi$
$751$	−22.8284	+	39.5400i	−0.833021	+	1.44283i	−0.895631	+	0.444797i	$0.853276\pi$
$752$	−5.24264	−	9.08052i	−0.191179	−	0.331132i
$753$	−31.5563	−	54.6572i	−1.14998	−	1.99182i
$754$	−5.08579	+	8.80884i	−0.185213	+	0.320799i
$755$	−9.21320			−0.335303
$756$		0			0
$757$	8.34315			0.303237			0.151618	−	0.988439i	$-0.451552\pi$
$757$	8.34315			0.303237			0.151618	+	0.988439i	$0.451552\pi$
$758$	−13.9350	+	24.1362i	−0.506143	+	0.876665i
$759$	7.53553	+	13.0519i	0.273523	+	0.473755i
$760$	−0.171573	−	0.297173i	−0.00622360	−	0.0107796i
$761$	15.4853	−	26.8213i	0.561341	−	0.972271i	−0.436039	−	0.899928i	$-0.643619\pi$
$761$	15.4853	−	26.8213i	0.561341	−	0.972271i	0.997380	−	0.0723433i	$-0.0230477\pi$
$762$	37.9706			1.37553
$763$		0			0
$764$	−7.17157			−0.259458
$765$	3.02944	−	5.24714i	0.109530	−	0.189711i
$766$	−3.19239	−	5.52938i	−0.115346	−	0.199785i
$767$	−10.6924	−	18.5198i	−0.386080	−	0.668710i
$768$	−1.20711	+	2.09077i	−0.0435577	+	0.0754442i
$769$	−22.9706			−0.828340			−0.414170	−	0.910200i	$-0.635928\pi$
$769$	−22.9706			−0.828340			−0.414170	+	0.910200i	$0.635928\pi$
$770$		0			0
$771$	60.6985			2.18600
$772$	−10.9497	+	18.9655i	−0.394090	+	0.682584i
$773$	−10.9706	−	19.0016i	−0.394584	−	0.683439i	0.598464	−	0.801150i	$-0.295778\pi$
$773$	−10.9706	−	19.0016i	−0.394584	−	0.683439i	−0.993048	+	0.117710i	$0.962445\pi$
$774$	8.00000	+	13.8564i	0.287554	+	0.498058i
$775$	9.31371	−	16.1318i	0.334558	−	0.579472i
$776$	3.82843			0.137433
$777$		0			0

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1078 = 2 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1078.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-1.20711 - 2.09077i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.292893 + 0.507306i) q^{5} +2.41421 q^{6} +1.00000 q^{8} +(-1.41421 + 2.44949i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-1.20711 - 2.09077i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.292893 + 0.507306i) q^{5} +2.41421 q^{6} +1.00000 q^{8} +(-1.41421 + 2.44949i) q^{9} +(-0.292893 - 0.507306i) q^{10} +(-0.500000 - 0.866025i) q^{11} +(-1.20711 + 2.09077i) q^{12} +3.82843 q^{13} +1.41421 q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.82843 + 3.16693i) q^{17} +(-1.41421 - 2.44949i) q^{18} +(-0.292893 + 0.507306i) q^{19} +0.585786 q^{20} +1.00000 q^{22} +(3.12132 - 5.40629i) q^{23} +(-1.20711 - 2.09077i) q^{24} +(2.32843 + 4.03295i) q^{25} +(-1.91421 + 3.31552i) q^{26} -0.414214 q^{27} +2.65685 q^{29} +(-0.707107 + 1.22474i) q^{30} +(-2.00000 - 3.46410i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-1.20711 + 2.09077i) q^{33} -3.65685 q^{34} +2.82843 q^{36} +(4.70711 - 8.15295i) q^{37} +(-0.292893 - 0.507306i) q^{38} +(-4.62132 - 8.00436i) q^{39} +(-0.292893 + 0.507306i) q^{40} +5.41421 q^{41} -5.65685 q^{43} +(-0.500000 + 0.866025i) q^{44} +(-0.828427 - 1.43488i) q^{45} +(3.12132 + 5.40629i) q^{46} +(-5.24264 + 9.08052i) q^{47} +2.41421 q^{48} -4.65685 q^{50} +(4.41421 - 7.64564i) q^{51} +(-1.91421 - 3.31552i) q^{52} +(-3.94975 - 6.84116i) q^{53} +(0.207107 - 0.358719i) q^{54} +0.585786 q^{55} +1.41421 q^{57} +(-1.32843 + 2.30090i) q^{58} +(-2.79289 - 4.83743i) q^{59} +(-0.707107 - 1.22474i) q^{60} +(5.91421 - 10.2437i) q^{61} +4.00000 q^{62} +1.00000 q^{64} +(-1.12132 + 1.94218i) q^{65} +(-1.20711 - 2.09077i) q^{66} +(-1.37868 - 2.38794i) q^{67} +(1.82843 - 3.16693i) q^{68} -15.0711 q^{69} -11.0711 q^{71} +(-1.41421 + 2.44949i) q^{72} +(-4.70711 - 8.15295i) q^{73} +(4.70711 + 8.15295i) q^{74} +(5.62132 - 9.73641i) q^{75} +0.585786 q^{76} +9.24264 q^{78} +(6.62132 - 11.4685i) q^{79} +(-0.292893 - 0.507306i) q^{80} +(4.74264 + 8.21449i) q^{81} +(-2.70711 + 4.68885i) q^{82} +12.1421 q^{83} -2.14214 q^{85} +(2.82843 - 4.89898i) q^{86} +(-3.20711 - 5.55487i) q^{87} +(-0.500000 - 0.866025i) q^{88} +(6.24264 - 10.8126i) q^{89} +1.65685 q^{90} -6.24264 q^{92} +(-4.82843 + 8.36308i) q^{93} +(-5.24264 - 9.08052i) q^{94} +(-0.171573 - 0.297173i) q^{95} +(-1.20711 + 2.09077i) q^{96} +3.82843 q^{97} +2.82843 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 2 q^{3} - 2 q^{4} - 4 q^{5} + 4 q^{6} + 4 q^{8}+O(q^{10}) \) 4 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 - 4 * q^5 + 4 * q^6 + 4 * q^8	\( 4 q - 2 q^{2} - 2 q^{3} - 2 q^{4} - 4 q^{5} + 4 q^{6} + 4 q^{8} - 4 q^{10} - 2 q^{11} - 2 q^{12} + 4 q^{13} - 2 q^{16} - 4 q^{17} - 4 q^{19} + 8 q^{20} + 4 q^{22} + 4 q^{23} - 2 q^{24} - 2 q^{25} - 2 q^{26} + 4 q^{27} - 12 q^{29} - 8 q^{31} - 2 q^{32} - 2 q^{33} + 8 q^{34} + 16 q^{37} - 4 q^{38} - 10 q^{39} - 4 q^{40} + 16 q^{41} - 2 q^{44} + 8 q^{45} + 4 q^{46} - 4 q^{47} + 4 q^{48} + 4 q^{50} + 12 q^{51} - 2 q^{52} + 4 q^{53} - 2 q^{54} + 8 q^{55} + 6 q^{58} - 14 q^{59} + 18 q^{61} + 16 q^{62} + 4 q^{64} + 4 q^{65} - 2 q^{66} - 14 q^{67} - 4 q^{68} - 32 q^{69} - 16 q^{71} - 16 q^{73} + 16 q^{74} + 14 q^{75} + 8 q^{76} + 20 q^{78} + 18 q^{79} - 4 q^{80} + 2 q^{81} - 8 q^{82} - 8 q^{83} + 48 q^{85} - 10 q^{87} - 2 q^{88} + 8 q^{89} - 16 q^{90} - 8 q^{92} - 8 q^{93} - 4 q^{94} - 12 q^{95} - 2 q^{96} + 4 q^{97}+O(q^{100}) \) 4 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 - 4 * q^5 + 4 * q^6 + 4 * q^8 - 4 * q^10 - 2 * q^11 - 2 * q^12 + 4 * q^13 - 2 * q^16 - 4 * q^17 - 4 * q^19 + 8 * q^20 + 4 * q^22 + 4 * q^23 - 2 * q^24 - 2 * q^25 - 2 * q^26 + 4 * q^27 - 12 * q^29 - 8 * q^31 - 2 * q^32 - 2 * q^33 + 8 * q^34 + 16 * q^37 - 4 * q^38 - 10 * q^39 - 4 * q^40 + 16 * q^41 - 2 * q^44 + 8 * q^45 + 4 * q^46 - 4 * q^47 + 4 * q^48 + 4 * q^50 + 12 * q^51 - 2 * q^52 + 4 * q^53 - 2 * q^54 + 8 * q^55 + 6 * q^58 - 14 * q^59 + 18 * q^61 + 16 * q^62 + 4 * q^64 + 4 * q^65 - 2 * q^66 - 14 * q^67 - 4 * q^68 - 32 * q^69 - 16 * q^71 - 16 * q^73 + 16 * q^74 + 14 * q^75 + 8 * q^76 + 20 * q^78 + 18 * q^79 - 4 * q^80 + 2 * q^81 - 8 * q^82 - 8 * q^83 + 48 * q^85 - 10 * q^87 - 2 * q^88 + 8 * q^89 - 16 * q^90 - 8 * q^92 - 8 * q^93 - 4 * q^94 - 12 * q^95 - 2 * q^96 + 4 * q^97

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